Linearly implicit methods for the nonlinear Schrödinger equation in nonhomogeneous media

DOI10.1016/S0096-3003(01)00220-XzbMath1024.65083MaRDI QIDQ1855865

Juan I. Ramos

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

numerical experimentsnonlinear Schrödinger equationerror boundsperturbation methodsinverse scatteringlinearly implicit finite difference methodsdamping and pumpingsolutions in finite linesvariable refraction index

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients ⋮ Simulation of coherent structures in nonlinear Schrödinger-type equations ⋮ A dual-reciprocity boundary element solution of a generalized nonlinear Schrödinger equation ⋮ An exponential spline solution of nonlinear Schrödinger equations with constant and variable coefficients ⋮ Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method ⋮ Interactions of two co-propagating laser beams in underdense plasmas using a generalized peaceman-Rachford ADI form ⋮ Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients

Cites Work

• Unnamed Item
• The numerical treatment of the nonlinear Schrödinger equation
• Numerical experience with the nonlinear Schrödinger equation
• Analytical and numerical aspects of certain nonlinear evolution equations. IV: Numerical, modified Korteweg-de Vries equation
• Linearization methods for reaction-diffusion equations: 1-D problems
• Linearization methods for reaction-diffusion equations: Multidimensional problems
• Finite-difference solutions of a non-linear Schrödinger equation
• An explicit finite-difference scheme with exact conservation properties
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• A numerical scheme for the nonlinear Schrödinger equation
• Numerical solution of a nonlinear Klein-Gordon equation
• Transmission of solitons through random media
• Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• Perturbations of Solitons and Solitary Waves
• Optimal H¹ Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
• Dynamics of Semi-Discretizations of the Defocusing Nonlinear Schrödinger Equation
• Finite difference discretization of the cubic Schrödinger equation
• The inverse scattering transform: Semi-infinite interval
• A Nonlinear Difference Scheme and Inverse Scattering
• A numerical and theoretical study of certain nonlinear wave phenomena
• Soliton Evolution in the Presence of Perturbation
• Symplectic methods for the nonlinear Schrödinger equation

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